What is Moment: Definition and 1000 Discussions

In mathematics, the moments of a function are quantitative measures related to the shape of the function's graph. If the function represents mass, then the first moment is the center of the mass, and the second moment is the rotational inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.
For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem).
In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematically in terms of the moments of random variables.

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  1. W

    Moment Direction: 560sin30 (0.25) Explained

    Homework Statement why the moment 560sin30 (0.25) isn't in clockwise direction ? the horizontal component of the 560N force is directed to the left , causing the moment in clockwise direction, am i right ? I have made my sketch beside in the diagram ... Homework EquationsThe Attempt at a Solution
  2. imadrea

    How to devise moment of inertia formula of solid sphere?

    Homework Statement how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M. Homework Equations I=∫r2dm 2/5 MR^2 The Attempt at a Solution https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p i try to...
  3. G

    Anticlockwise Moment & Force Direction: Why the Change?

    Homework Statement in figure b , based on the direction of moment of anticlockwise is positive , i can say that -Tcos20 (7 sin 30 ) is a clockwise moment , so that the tension of rope should be acted in upward direction , so that the horizontal component of the force acted to the left to...
  4. minimario

    Moment of Inertia of Spherical Shell

    Homework Statement Find the moment of inertia of a spherical shell (hollow) with mass M and radius R. Homework Equations ## I = \int r^2 dm ## The Attempt at a Solution This is method I use to find Moment of Inertia of solid sphere: We use circular cross sections. At some radius r...
  5. K

    Is the moment of inertia matrix a tensor?

    Homework Statement Is the moment of inertia matrix a tensor? Hint: the dyadic product of two vectors transforms according to the rule for second order tensors. I is the inertia matrix L is the angular momentum \omega is the angular velocity Homework Equations The transformation rule for a...
  6. T

    Moment and reaction of shaft - Statically Indeterminate

    A shaft of diameter 10 inch is supported by 3 ball bearings. An external force (F, given) from pulley (diameter not given) also acts on the shaft. The supports are subjected to bending load (moment and transverse shear) and torsion load due to pulley. Yield Stress at Tension given. Assume no...
  7. B

    Why does not dipole moment depend on coordinates system?

    Homework Statement This is problem 6.5 in Griffiths EM. I can't understand why dipole moment does not depend on coordinate systems. Homework EquationsThe Attempt at a Solution
  8. E

    Help with 2nd moment of inertia

    If a beam's y-y axis lies in the plane of the paper, do I use Ixx or Iyy from sections table?
  9. W

    M2 Point C Moment Calculation: Why is it Not the Same as Book?

    Homework Statement for M2 , if i take the moment at pont C , then my ans would be (0.3i) x ((125X(3/5) j +125(4/5) k )= 30j +22.5k Which is not same with the book which use moment about D . why ? Is the value at the triangle at te upper part incorrect (circle part) ? Homework EquationsThe...
  10. G

    Finding theta when moment is max

    Homework Statement to achieve max moment , the 4 kN must br perpendiclar to 20m , right ? so, i formed a cloased triangle and use sine rule to find the tetha , 25/ sin90 = 4/sin tetha , i gt my tetha = 9.2 degree , but the ans given is 33.6degree i gt max moment = 80Nm Homework EquationsThe...
  11. W

    Finding angle for specific moment

    Homework Statement i have question with part B my working is 13.2 cos tetha (0.86x10^-3)+ 13.2 sin tetha (1.22x10^-3) = 1.95 i gt stucked here. how to proceed? i only have one equation , how to solve two unknown ? Homework EquationsThe Attempt at a Solution
  12. H

    Moment of Inertia and Bike stability

    So is a Bike driver stable when the bike is running because the bike wheels has a certain moment of inertia about the horizontal axis ,which might alter(mi gets lesser) if the direction of the axis changes ? Thanks in advance
  13. W

    Moment about a point using graph paper

    Homework Statement the ans given is 95Nm , but i gt 80.9Nm , which part i did wrongly ? Homework EquationsThe Attempt at a Solution 20(4) -39(5/surd 26(3)) +39(1/surd26)(1) -60(3/5)(1)+60(4/5)(3) =80.9[/B]
  14. W

    What is the Correct Magnitude of P in a System of Forces?

    Homework Statement In this question , I'm asked to find the magnitude of P . Homework EquationsThe Attempt at a Solution Resultant moment about O = -10cos30 (4√3) -10sin 30 (10 +15sin30(2) + 15cos30(4√3) -10cos30(4√3) -10sin30(4) -15cos30(4√3) -15sin30(7) +10cos30(4√3) +10sin30(11) +P cos...
  15. M

    Strength of materials/Max bending moment

    Homework Statement It's been a while since I've done this, it's essentially a strength of materials problem in my mechanical analysis class so I haven't worked problems like these in quite a a while. I'm fairly confident I've done it right however I was hoping someone might be able to confirm...
  16. M

    Transition dipole moment: cause or result of interaction?

    According to the wikipedia article about the transition dipole moment: When an atom or molecule interacts with an electromagnetic wave of frequency , it can undergo a transition from an initial to a final state of energy difference through the coupling of the electromagnetic field to the...
  17. G

    Moment at a point when the object is sliding

    Homework Statement i can't understand why when the total moment at B is positive , the object is not sliding ? can someone help to explain ? Homework EquationsThe Attempt at a Solution
  18. G

    Solving a Moment Equation: Understanding the Relationship with AD

    Homework Statement Inq this question, I am given that the u dot ( rb x tb + re x w) =0. I knew that the rb x tb give a resultant moment pointed inside the book , which is parallel to AB... Then it cross with r AD, we will get the resultant moment. But when re x w , I will gt the moment...
  19. Y

    Tension on cable CD when moment on A is Zero.

    Homework Statement Looking for the tension in cable Tcd when the moment on A is equal to 0. P1 = 73N. I’ve had several attempts but I can’t seem to obtain the answer, which is 110,8 N. Can anyone help me with this question? Homework EquationsThe Attempt at a Solution
  20. W

    Calculating the Moment of Inertia of a loaded flywheel

    Hi, I need to calculate the moment of inertia of this flywheel so I can calculate the torque I need. T= I*alpha Attached is an image of the flywheel the cam follower that will be attached to the shaft (left shaft in this picture). When calculating the Moment of Inertia, what mass do I use...
  21. A

    Statics - Moment using both vector and scalar approaches

    Homework Statement Homework Equations Mo=Fd Mo=r x F The Attempt at a Solution Alright guys, I did the whole process but I'm pretty sure I just made a little bump somewhere in my calculations which screwed up my answers. First I found everything I could find OA = 350j, so the unit vector...
  22. G

    Direction of Moment: 1200N at A- Clockwise or Counterclockwise?

    Homework Statement Why shouldn't the direction of moment for 1200n at A =clockwise? Why the book gave counterclockwise? Homework EquationsThe Attempt at a Solution
  23. J

    Determine the resultant couple moment

    Homework Statement 4-70 Two couples act on the beam. If F=125 lb. determine the resultant couple moment. Homework Equations M=Fd The Attempt at a Solution I know CW is + and CCW is - ...and that is determined in the final answer, I know the solution is taking Forces times the distance...
  24. KastorPhys

    Moment of Inertia of a sphere with different methods

    Hi everyone, I am trying to find out the Moment of Inertia of a sphere which is all known to be 2/5(m)(r^2) I calculate this in 2 ways. One by triple integration and one by disk method. From the textbooks, moment of inertia should be in the form, dI = (r^2) dm, However, the textbook, University...
  25. G

    Can Torque Be Applied to an Object Through Linear Forces Alone?

    Homework Statement Why the moment isn't=15* 3Nm? Since we are taking moment about point O...it's 3m away from O Homework EquationsThe Attempt at a Solution
  26. G

    Direction of rotation of moment

    Homework Statement IMO , the M2 and M1 should rotate clockwise, and the moment should point downwards based on right hand grip rule . Why the book gave in in other way ? Homework EquationsThe Attempt at a Solution
  27. P

    Finding Static Equilibrium: Solving for Unknown Angles

    Can anyone help me with this question! I know to solve this problem, you have to set ΣF and ΣM =0, but what do you do with angle? (It's P.31 in the bottom)
  28. G

    Direction of rotation of moment

    Homework Statement for the 400cos45 force , i think it should rotate anticlockwise, am i right? but the book gave it is rotated counterclockwise... Homework EquationsThe Attempt at a Solution
  29. G

    Direction of Moment: Is Book Correct?

    Homework Statement IMO, the direction of moment of both F1 and F2 should point inside the paper , and rotate clockwise , am i right ? but the book gave different things... which is correct? Homework EquationsThe Attempt at a Solution
  30. gacb17424

    Find reactions at supports and bending/shear/axial diagrams

    Homework Statement Force by uniform loading = 20(5) = 100kN Vertical component of the uniform loading = 20(5)(3/5) = 60kN Horizontal component of the loading = 20(5)(4/5) = 80kN vertical reaction at roller support = Vr vertical reaction at pin support = Vp Homework Equations Fx=0, Fy=0...
  31. D

    Calculating Moment & Horizontal Force at O for 100 lb Force

    Homework Statement A 100 lb vertical force is applied to the end of a lever, which is attached to a shaft at O. Determine (a) the moment of the 100 lb force about O (b) the horizontal force applied at a that creates the same moment about O. Homework EquationsThe Attempt at a Solution I know...
  32. G

    Why is the direction of M_0 (r x F) out of the paper?

    Homework Statement I can't understand why the M_0 ( M_0 = r x F)is pointing in the direction out of the paper ? Homework EquationsThe Attempt at a Solution
  33. R

    What is [s]motion[/s] moment of inertia of an equilateral triangle?

    I am unable to find it.
  34. L

    Find Moment Around A with 3D Vectors: B & C

    Homework Statement A (0,0,0) B(5,6,1) C(3,0,4) |F|= 1919N Homework EquationsThe Attempt at a Solution Cartesian: B= {5i + 6j + 1k} C= {3i + 4k} rCB ={2i + 6j - 3k} |rCB| = sqrt(22 + 62 + 32) = 7 Unit vector = rCB / |rCB| = {2/7i + 6/7j - 3/7k} F = |F| * Unit vector = 1919 {2/7i + 6/7j...
  35. P

    How to get a # out of moment of the parallel axis theorm

    The question is : four masses shown in figure 12.14 (Knight 12.14) are connected by massless, rigid rods. (see attached fig) A) find the coordinates of the center of mass B) find the moment of inertia about a diagonal mass that passed through B and D so I got part a right by setting the x-y...
  36. B

    Setting up a Double Integral for Moment of Inertia

    Homework Statement >Problem:<br>Find the Moment of Inertia of a circular disk of uniform density about an axis which passes through the center and makes an angle of $\dfrac{\pi}{6}$ with the plane of the disc. Homework Equations Moment of Inertia ($I$) is $$\int r^2dm$$ where $r$ is the...
  37. gracy

    Electric dipole moment problem

    Homework Statement find the electric dipole moment of the system shown in figure Homework Equations In the simple case of two point charges, one with charge +q and the other one with charge −q, the electric dipole moment p is: where d is the displacement vector pointing from the negative...
  38. M

    Calculating Moments: Forces on a Ratchet Wrench

    Homework Statement Two 20 lb forces are applied to a ratchet wrench down at A and up at B to loosen bolt β. Find the sum of the moments of the two forces about the axis (x) of the bolt. Homework Equations What are the moments at point A, B, and Q? How do I find the moment about the x-axis and...
  39. 24forChromium

    Moment of inertia of a cylinder in unusual position

    See image. It would be better if you can show me the calculation process. EDIT: the axis of rotation goes right through the centre of the cylinder. NEVER MIND! GOT IT!
  40. J

    Moment of Inertia of multiple bodies in contact

    What is the overall moment of inertia of many cylinders in contact, where each is rotated about an axis through its center of mass. For example, a set of rollers. (See picture)
  41. Z

    Different formulae for moment of inertia

    I know the formula for moment of inertia is but there are I = MR^2 but there are also formulae for different objects as shown in the picture. So, how and when do you use I = MR^2 ? Just in case of (a)? Thanks!
  42. Priyadarshini

    Moments of a Ladder Propped Up Against A Wall

    Homework Statement A uniform ladder rests against a vertical wall where there is negligible friction. The bottom of the ladder rests on rough ground where there is friction. The top of the ladder is at a height h above the ground and the foot of the ladder is at a distance 2a from the wall...
  43. A

    Moment of inertia about tangent of a hoop

    The hoop has radius R. I used the same way to plot the axis for the hoop: ##l^2 = r^2= 4R^2cos\theta## since: ##r=2Rcos\theta## 2\rho \int_{0}^{\frac{\pi}{2}} r^2 r d\theta 2\rho \int_{0}^{\frac{\pi}{2}} 8R^3 cos^3\theta d\theta answer is \frac{32}{3}R^3\rho , and its wrong using the...
  44. C

    Checking Bending Moment of Hub Connectors

    hi Gents, i am checking bending moment for hub connector. The manufacturer send me two values of maximum bending moment- one value due to primary load and one value due to primary load + secondary load. If you have any experience on checking bending moment of hub, please advise what value we...
  45. C

    Why is it that light has momentum?

    The way that I understand it is this. But correct me if I'm wrong. Because P=m*v, sense infinity * 0 in calculus is 1, and because the speed of light is the limit of velocity, we can express it as infinity, so p = 0 kg * infinity m/s. Is that at all right?
  46. D

    Atomic dipole moment for a superposition state

    Hi all, I'm trying to understand how to calculate the time dependent expectation value of the atomic dipole moment for a superposition state, and I have a good guess to check with you. Say we have \psi = \frac{1}{\sqrt{2}} \left[ \psi _{100} + \psi _{310} \right] at t = 0. Then, for t > 0: \Psi...
  47. S

    B Control moment gyroscope design - question

    Hi all, Like a lot of folk on here I am interested in the idea of a CMG used to stabalise a single track vehicle.<< Link to CMG info added by Mentor >> https://en.wikipedia.org/wiki/Control_moment_gyroscope I have designed this; the pink discs spin in opposite directions and the pendulum...
  48. Jimbob999

    Find magnetic dipole moment of coiled wire

    Homework Statement A 45-m long wire is coiled so that it makes a coil containing 100 circular loops, one on top of the other. If the wire carries a current of 13 A, what is the magnetic dipole moment of the coil? 21 A·m2 6.7 A·m2 3.3 A·m2 2.6 A·m2 1.2 A·m2 Homework Equations B(z) = u0/2pi...
  49. P

    Trouble Understanding Moment Calculations?

    Hi, I am having trouble understanding how the signs were obtained in the moment calculation. When I imagine the 600 N force acting on the moment arm, it moves CW which would give it a negative value. When I solve the problem I end up reviving Ay and Cy values that are swapped with the book.
  50. V

    Finding Forces in Truss Members for Solving Truss Problems

    Homework Statement Homework EquationsThe Attempt at a Solution First i Found the external forces. Ax =0 , Ay = 8Kn, Jy=8Kn and P = -16Kn Then i took moment about point G to eliminate FH and EG and so was able to find CH = 14.66Kn. I am kind of stuck on how to tackle the problem further...
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